Problem: Jerry played with $3$ friends today, all at different times. He played with Tommy for $1\dfrac{7}{8}$ hours, then Nathan for $1\dfrac{3}{4}$ hours, then Chris for $\dfrac{3}{2}$ hours. How many hours did Jerry play with his $3$ friends today?
Solution: To find the total number of hours that Jerry played with his friends, we need to add. $1\frac{7}{8}$ $1\frac{3}{4}$ $\frac{3}{2}$ Tommy Nathan Chris Hours spent playing ${1\dfrac78} + {1\dfrac34} + \dfrac32} = \text{ hours spent playing}$ Our denominators need to be the same so we can add. What is the least common multiple for the denominators $8$, ${4}$, and $2}$ ? The least common multiple of $8$, ${4}$, and $2}$ is ${8}$. $\dfrac{{3}\times 2}{{4}\times 2} = {\dfrac{6}{8}}$ $\dfrac{3}\times 4}{2}\times 4} = \dfrac{12}{8}}$ Now we can add our fractions. $\begin{aligned} &{1} &{\dfrac7{8}}\\\\ &{1}&{\dfrac{6}{8}}\\ +&0}&\dfrac{12}{8}}\\ \hline\\ &&{\dfrac{25}{8}}\\ \end{aligned}$ We can replace $ {\dfrac{25}{8}}$ with $3 {\dfrac{1}{8}}$. $\begin{aligned} &3\\ &{1} &{\dfrac7{8}}\\\\ &{1}&{\dfrac{6}{8}}\\ +&0}&\dfrac{12}{8}}\\ \hline\\ &&{\dfrac{1}{8}}\\ \end{aligned}$ Now we can add our whole numbers. $\begin{aligned} &3\\ &{1} &{\dfrac7{8}}\\\\ &{1}&{\dfrac{6}{8}}\\ +&0}&\dfrac{12}{8}}\\ \hline\\ &5&{\dfrac{1}{8}}\\ \end{aligned}$ Jerry played with his three friends for $\dfrac{41}{8}$ hours today. This can also be written as $5\dfrac{1}{8}$ hours.